English

Le principe de Hasse pour les intersections de deux quadriques dans $\mathbb{P}^7$

Algebraic Geometry 2024-06-07 v4

Abstract

We prove the Hasse principle for a smooth proper model of a geometrically integral non-conical intersection of two quadrics in the projective space of dimension 7 over a number field. This result generalizes the result of Heath-Brown who established the statement in the smooth case. Our argument is built upon the ideas of Colliot-Th\'el\`ene and the fibration method for zero-cycles in the form of Harpaz-Wittenberg.

Keywords

Cite

@article{arxiv.2305.00313,
  title  = {Le principe de Hasse pour les intersections de deux quadriques dans $\mathbb{P}^7$},
  author = {Alexander Molyakov},
  journal= {arXiv preprint arXiv:2305.00313},
  year   = {2024}
}

Comments

Paper in French, 21 pages